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- Erik D. Demaine, Martin L. Demaine, +4 authors Diane L. Souvaine
- Natural Computing
- 2007

We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are motivated by a practical nanofabrication scenario through protein-based bioengineering. Staging allows us to break through… (More)

- Sarah Cannon, Erik D. Demaine, +5 authors Andrew Winslow
- ArXiv
- 2012

We study the difference between the standard seeded model of tile self-assembly, and the " seedless " two-handed model of tile self-assembly. Most of our results suggest that the two-handed model is more powerful. In particular, we show how to simulate any seeded system with a two-handed system that is essentially just a constant factor larger. We exhibit… (More)

- Esther M. Arkin, Michael A. Bender, +4 authors Steven Skiena
- Comput. Geom.
- 2001

We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds; the simplest one-layer simple fold rotates a portion of paper about a crease in the paper by ±180 •. We first consider… (More)

A hinged dissection of a set of polygons S is a collection of polygonal pieces hinged together at vertices that can be rotated into any member of S. We present a hinged dissection of all edge-to-edge gluings of n congruent copies of a polygon P that join corresponding edges of P. This construction uses kn pieces, where k is the number of vertices of P. When… (More)

We study a popular puzzle game known variously as Clickomania and Same Game. Basically, a rectangular grid of blocks is initially colored with some number of colors, and the player repeatedly removes a chosen connected monochromatic group of at least two square blocks, and any blocks above it fall down. We show that one-column puzzles can be solved, i.e.,… (More)

- Erik D. Demaine, Martin L. Demaine, Craig S. Kaplan
- CCCG
- 2000

We introduce and characterize a new class of polygons that models wood, stone, glass, and ceramic shapes that can be cut with a table saw, lapidary trim saw, or other circular saw. In this model, a circular saw is a line segment (in projection) that can move freely in empty space, but can only cut straight into a portion of material. Once a region of… (More)

- Byoungkwon An, Shuhei Miyashita, +6 authors Daniela Rus
- 2014 IEEE International Conference on Robotics…
- 2014

This paper presents an end-to-end approach for creating 3D shapes by self-folding planar sheets activated by uniform heating. These shapes can be used as the mechanical bodies of robots. The input to this process is a 3D geometry (e.g. an OBJ file). The output is a physical object with the specified geometry. We describe an algorithm pipeline that (1)… (More)

This paper investigates the popular card game UNO R from the viewpoint of algorithmic combinatorial game theory. We define simple and concise mathematical models for the game, including both cooperative and uncooperative versions, and analyze their computational complexity. In particular, we prove that even a single-player version of UNO is NP-complete,… (More)

- Erik D. Demaine, Martin L. Demaine, Michael Hoffmann, Joseph O'Rourke
- Comput. Geom.
- 2003

We prove NP-hardness of a wide class of pushing-block puzzles similar to the classic Sokoban, generalizing several previous results [5, 6, 9, 10, 15, 17]. The puzzles consist of unit square blocks on an integer lattice; all blocks are movable. The robot may move horizontally and vertically in order to reach a specified goal position. The puzzle variants… (More)

- Erik D. Demaine, Martin L. Demaine, Rudolf Fleischer
- Theor. Comput. Sci.
- 2002

Clobber is a new two-player board game. In this paper, we introduce the 1-player variant Solitaire Clobber where the goal is to remove as many stones as possible from the board by alternating white and black moves. We show that a checkerboard configuration on a single row (or single column) can be reduced to about n/4 stones. For boards with at least two… (More)